CASIMATTER
(C)1999 Alan M. Schwartz
Acceleration versus applied force is inertial mass; acceleration
in a gravitational field is gravitational mass. The Equivalence
Principle asserts the masses are indistinguishable. General
Relativity posits gravitation as minimal paths (geodesics) traced
along the shape of space, but neglects inertia. Bernhard Haisch,
Hal Puthoff, Alfonso Rueda, and other stochastic electrodynamics
fans propose inertia's origin http://www.jse.com/haisch/zpf.html
The quantum vacuum has zero point fluctuations. Accelerating
within ZPF induces proportional resistance - inertia (Phys. Rev.
A 49 678 (1994), Science 263(5147) 612 (1994)).
Classical vacuum contains neither mass nor energy. Heisenberg
Uncertainty Principle in the quantum vacuum demands the product
of uncertainties of energy and time be a small but finite number.
The classical harmonic oscillator includes an uncertainty of 0.5
photon/allowed electromagnetic mode. Where do vacuum ZPF hide?
ZPF explain the Lamb shift, electron anomalous g-factor, Rabi
oscillations (single atom laser), and Casimir effect. ZPF do not
appear Doppler shifted and are Lorenz-invariant: intensity varies
as the cube of ZPF frequency (or inverse cube of its wavelength).
The grain of space appears near 10^(-33) cm, the Planck length.
Integrating intensity over all possible frequencies gives 10^94
gm/cm^3. Nuclear density is 2x10^14 gm/cm^3.
Accelerating within ZPF may elicit inertia. Screening ZPF may
separate inertial and gravitational masses if gravity is not ZPF-
related. If ZPF mediates both the Equivalence Principle prevails
(Phys. Rev. A 39 2333 (1989), Ibid. 47 3454 (1993));
(pi)c^5 2(pi)(lambda)^2c^3
Newton's G = ---------------- = -------------------
(h-bar)(omega)^2 h
(2)(3.14159)([(1.61605x10^(-33) cm)^2](2.99792x10^10 cm/sec)^3
= --------------------------------------------------------------
(6.6260755x10^(-27) erg-sec)
G = 6.67259x10^(-8) erg-cm/g^2
where c=lightspeed, (h-bar) is Planck's constant (6.6260755x10^(-
27) erg-sec) divided by 2(pi), and omega is the frequency of the
Planck wavelength (lambda), 1.61605x10^(-33) cm. There is a
debate over the presence of an additional factor of pi which, as
the Planck constant is expressed in terms of G, would rescale the
Planck length to 9.1176x10^(-34), a factor of sqrt(pi) smaller.
Call ZPF-depleted matter "Casimatter." If unified, Casimatter's
measured mass and weight still would be too small for the atoms
contained. Differential mass measurement before and after
thermal (700 C for aluminum) or other Casimatter disruption is
problematic. Chemical determination is insufficiently sensitive.
If mass and weight are not unified, can the Equivalence Principle
be finessed? Mass can fall too slowly - feathers falling in air.
Mass cannot free fall in vacuum too quickly, maybe.
ZPF is radiation, as in photons and waves. There is a node at a
perfectly electrically conductive reflective surface. Given two
plane parallel grounded metal mirrors in close apposition (narrow
gap) without an optically absorbing medium between them,
1) Only integral multiples of half wavelengths are resonantly
allowed for radiation with half wavelengths equal to the gap or
smaller. Longer wavelengths are absolutely excluded (etalon -
the more reflections the tighter the specification to 20% of all
shorter wavelengths also excluded), and
2) Radiation whose half wavelength exceeds the gap is excluded.
Unaltered ZPF outside the gap pushes in, attenuated ZPF in the
gap pushes out. The plates appear to attract varying inversely
with the fourth power of their separation - the Casimir effect.
H.B.G. Casimir, Proc. Kon. Ned. Akad. Wetensch. B51 793 (1948)
Contemporary Physics 33(5) 313 (1992)
Sov. Phys.-Dokl. 12(11) 1040 (1968)
Proc. Royal Soc. A 312 435 (1969)
Ann. Phys. (NY) 56 474 (1970)
Phys. Rev. E 48(2) 1562 (1993)
Edward G. Harris, "A Pedestrian Approach to Quantum Field
Theory," Wiley-Interscience, NY 1972, pp. 108-9
Measured to within 5% of theory, Phys. Rev. Lett. 78 5 (1996)
Phys. Rev. Lett. 81 4549 (1998)
Measured to within 1% of theory, Phys. Rev. A 59(5) R3149 (1999)
Imperfect mirrors, Phys. Rev. Lett. 81 3815 (1998)
Temperature above 0 K, Phys. Rev. A 57 1870 (1998)
Curved mirrors, Amer. J. Physics 65 381 (1997))
Spherical dielectrics, J. Phys. A: Math. Gen. 32 535 (1999)
With a ZPF wavelength limit of 10^(-33) centimeter (remember -
intensity varies as the inverse CUBE of the wavelength!) and a
practical reflection limit of around 10-(5) cm gap for aluminum
at its plasmon frequency cutoff, how much eldritch squeeze
obtains under ideal conditions?
A(pi)^2(h-bar)c
Fc = ---------------
(240)a^4
where A is area; "a" is the transparent separation of parallel
flat 100% conductive 100% reflective grounded plates at 0 K;
"h-bar" is Planck's constant divided by 2(pi); "c" is lightspeed.
If "a" is measured in micrometers the Casimir force is (0.01300
dyne/cm^2)/a^4 or (1.3x10^(-7) newton/cm^2)/a^4. An average
apple weighs a newton (coincidence?). A 500 nm (wavelength of
green light) gap gives 0.208 dyne/cm^2. A 100 nm gap (extreme
ultraviolet approaching soft x-ray) gives 130 dyne/cm^2 (a milli-
apple/cm^2). That is 33 times the weight of aluminum foil/cm^2.
Correction factors obtain for two dielectric plates (dd) or one
metal and one dielectric (md) plate (where e is the dielectric
constant; Phys. Rev. B. 30(4) 1700 (1984), JETP 2 73 (1956)):
Fc(e-1)^2 Fc(e-1)
Fdd = -----------f(dd) Fmd = ---------f(md)
(e+1)^2 (e+1)
e <3.5 4 5 8 10 25 50 infinity
----------------------------------------------------------
f(dd) 0.35 0.38 0.38 0.4 0.43 0.5 0.6 1.0
f(md) 0.48 0.5 0.52 0.55 0.58 0.7 0.8 1.0
How can bulk matter exclude ZPF? Aluminum, density 2.7 g/cm^3,
is the only metal amply reflecting deep into the ultraviolet, 93%
between 100 and 120 nm. Magnesium fluoride is a vacuum-deposited
dielectric transparent in the deep UV, 80% transmittance at 115
nm (http://www.crystran.co.uk/). Go much deeper (10.9 eV; J.
Appl. Phys. 38 1701 (1967)) and photons are energetic enough to
be absorbed by exciting electronic transitions. Magnesium
fluoride has density 3.177 g/cm^3 and a refractive index of 1.63
at 121 nm. Imagine a flat, wide ring within a two sector vacuum
deposition chamber. Resistance heating deposits 10 nm/sec Al and
2 nm/sec MgF2. High frequency magnetron sputtering is much
faster. A 30 second/paired layer deposition cycle with excellent
thickness control is entirely nominal.
One sector continuously deposits 70 nanometers of aluminum onto a
rotating ring ("AIP Handbook," 3rd Ed., Section 6, for 99+% of
theoretical reflectance vs transmission), promptly covered by 37
nanometers of magnesium fluoride in the other sector in a never
ending bifilar spiral. The optical path between aluminum mirrors
is the gap (37 nm) times refractive index (1.63) which is 60.3 nm
or 1/2(121 nm). Deposited thin film dielectrics tend to be
slightly porous with slightly lower refractive indices than bulk
material. Allow a safety margin for the 115 nm cutoff. Dice the
ring, release the backing, and hold sheets of Casimatter. Viewed
broadside Casimatter is an overcoated aluminum mirror (J. Opt.
Sci. Am. 51 719,913 (1961), ibid. 53 620 (1963)).
Casimatter, average density 2.86 g/cm^3, is 38 wt-% ZPF-depleted
magnesium fluoride. A centimeter thickness needs 93,460 layers
whose summed noise (dirt, non-ideal deposition) ruins flatness.
Ten paired layers deposited/minute is ten days of continuous
running. A human hair is 60 microns in diameter. Hair-thick
self-supporting if fragile Casimatter plates need 560 paired
layers. 560 is a large number, but not impossible in running
time (five hours at a leisurely pace) or physical structure.
Lithium fluoride goes to 110 nm with refractive index 1.777 and
density 2.639 g/cm^3 but is hygroscopic, degrading in humidity.
Vacuum deposit alternating layers of 31 nm LiF and 70 nm aluminum
to obtain Casimatter of average density 2.68 of which 30 wt-% is
ZPF-depleted lithium fluoride. A hair-thickness plate requires
595 paired layers with 40% more effect than the 121 nm etalon.
The Casimatter composite suffers from mismatch of linear thermal
coefficients of expansion of its components. As newly fabricated
Casimatter cools aluminum layers will shear deform from unequal
contraction versus dielectric layers:
LINEAR SHEAR ELASTIC
DENSITY RI EXPANSION MODULUS LIMIT
COMPONENT g/cm^3 121 nm x10^6/K GPa GPa
========================================================
Aluminum 2.70 23.1 24 0.13
MgF2 3.177 1.630 13.7 55 50.
LiF 2.639 1.624 37.0 55 11.
60:40 alloy 2.962 1.628 23.0
Rhenium 21.04 6.7 178
Does a miscible alloy of 60:40 MgF2:LiF exist and resist phase
separation to give a thermal expansion mismatch of only 0.1x10-
(6)/degree versus aluminum? Does it retain transparency in the
extreme ultraviolet? It is a minor vacuum deposition chore to
synthesize film alloy (bulk alloy crystallized via Stockbarger
directional solidification is unlikely) and perform measurements
of refractive index, transmission/wavelength, and thermal linear
expansion coefficient. Given weight-averaged refractive indices
for 121 nm (1.628) and densities (2.962), 37 nm of fluoride alloy
alternating with 70 nm of aluminum give Casimatter of average
density 2.79 of which 37 wt-% is ZPF-depleted fluoride alloy. A
hair-thickness plate requires 560 paired layers.
1) Thinning aluminum barriers with the next layer(s) taking
up the leakage reduces the net Casimir Effect faster than it
increases the ZPF-excluded mass ratio.
2) Extremely small optical gap fabrication is insufficient.
55 nm aluminum is transparent (refractive index of 0.753,
absorption coefficient of 0.021, reflectance of 0.02) but rhenium
is reflective (refractive index of 0.55, absorption coefficient
of 0.97, reflectance of 0.34). 80 nm of rhenium alternating with
36 nm of aluminum give Casimatter of average density 13.29
gm/cm^3 of which 5.5 wt-% is ZPF-depleted aluminum. With an
etalon gap ratio of 54/121 = 0.446 the ZPF exclusion will be 25.2
times as great for an overall bulk enhancement factor of 3.7
versus aluminum plus fluoride alloy, less reflectance and
transmittance inefficiencies which kill the idea. Mismatched
linear thermal coefficients of expansion of aluminum and rhenium
compromise the physical integrity of 520 bifilar layers summing
to 60 microns in thickness and square centimeters in extent.
3) Use aluminum as transparent spacer for a 10 nm gap and 30
nm of fluoride alloy as dielectric walls to give Casimatter of
average density 2.90 of which 23 wt-% is ZPF-depleted aluminum.
1500 bifilar layers sum to a 60 micron thickness. The gap would
be 1/12 as large: (.23/.37)(12^4)[(5.91^2)/(7.91^2)](.39) for
2800 times the ZPF exclusion versus the conservative case,
depending upon how thick a dielectric continuum constitutes a
"wall." Risky.
Given Casimatter plates thick as a human hair and a couple of
centimeters on a side, expected potential divergence of inertial
and gravitational masses will be very small - parts-per-billion
or less. Two sensitive analytical techniques are appropriate.
Fashion Casimatter into hollow corner cubes and drop them in a
vacuum chamber as one leg of an interferometer. Computer counts
of fringe shifts/time derives acceleration. Alternate with drops
of ordinary hollow corner cubes of the same dimensions and mass.
Dr. James Faller (Fallerj@Jila.Colorado.Edu) of the University of
Colorado has gravimeters of surpassing sensitivity and precision:
"Continuous gravity observations using Joint Institute for
Laboratory Astrophysics absolute gravimeters" J. Geophys. Res. 97
12437 (1992), J. Geophys. Res. 98(B3) 4619 (1993) A hundred JILA
installations measure gravity worldwide to a few microgals
(10^(-8)meter/sec^2; 1 gee = 980 microgals) precision.
Alternatively, Play gravitation (gravitational mass) against
centripetal force (inertial mass) in an Eotvos balance,
Eotvos experiment Ann. Physik., 68, 11 (1922)
"Eotvos Balance" Am. J. Phys. 27(5) 336 (1959)
Scientific American 205(6) 84 (1961)
Phys. Rev. Lett. 59(6) 609 (1987)
What alternative view is possible? Blackbody radiation arises
from charged quantum oscillators in walls (Planck) or photon gas
statistics in cavities (Bose). The same answer obtains either
way, but which one is the correct interpretation? Yes.
The Feynman-Hellman theorem, Phys. Rev. 56 340 (1939), asserts
two reflective conductive plates' proximity causes redistribution
of charge. The force between the plates is classical, acting
between redistributed charges. The Casimir effect is modeled as
two enormous inert atoms (bound plasmas) inducing reciprocal
polarization and experiencing van der Waals attraction from an
integrated Lennard-Jones potential. No ZPF are required.
Casimir energy between two points is the free energy of two
quantized fluctuating dipole moments coupled by dipole-dipole
radiation interaction (zero frequency being static interaction).
This treatment exactly scales to the parallel dielectric plate
case (Physica A 153 420 (1988), ibid. 259 165 (1998)).
Casimatter could be an ice pick driven by a sledgehammer, or just
a big water balloon. Somebody has to do the experiments.